Preschoolers' repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current study was to examine the causal effects of repeating patterning and numeracy tutoring on repeating patterning,…

Preschoolers' repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current Study was to examine the causal effects of repeating patterning and numeracy tutoring on repeating patterning,…

Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…

This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

This study examined the influence of virtual manipulatives on different achievement groups during a teaching experiment in four fifth-grade classrooms. During a two-week unit focusing on two rational number concepts (fraction equivalence and fraction addition with unlike denominators) one low achieving, two average achieving, and one high…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

Activities with triangular, square, pentagonal, hexagonal, and octagonal numbers are briefly discussed. (MNS)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

Simple patterns both in mathematics and music are discussed. Several activities using standard instruments and handmade devices are described. (MNS)

Several experiences with palindrome numbers are given, each leading to the "Law of 11." Conjectures for the reader to consider are included. (MNS)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Stresses that powers are all based on geometric progressions which start at unity. Various patterns are discussed. (MNS)

Developing numerical relationships with calculators is emphasized. Calculators furnish some needed support for students as they investigate the value of fractions as the numerators or denominators change. An example with Logo programing for computers is also included. (MNS)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)